61. Number Theory: Diophantine Equations Developing A General 2nd Degree diophantine equation x^2 + p = 2^n. Methodsto solve these equations. Quadratic diophantine equation Solver. http://www.puredirectory.com/Science/Math/Number-Theory/Diophantine-Equations/

Number Theory: Diophantine Equations Home Science Math Number Theory : Diophantine Equations Equal Sums of Like Powers Fermat's Last Theorem google_ad_client = "pub-3272565765518472";google_alternate_color = "FFFFFF";google_ad_width = 336;google_ad_height = 280;google_ad_format = "336x280_as";google_ad_channel ="7485447737";google_color_border = "FFFFFF";google_color_bg = "FFFFFF";google_color_link = "0000FF";google_color_url = "008000";google_color_text = "000000"; Standard Listings Sets of numbers such that the product of any two is one less than a square. Diophantus found the rational set 1/16, 33/16, 17/4, 105/16; Fermat the integer set 1, 3, 8, 120. Bibliography on Hilbert's Tenth Problem Searchable, ~400 items. Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n Methods to solve these equations. Diophantine Equations Dave Rusin's guide to Diophantine equations. Diophantine Geometry in Characteristic p A survey by Jos Felipe Voloch. Diophantine m-tuples Sets with the property that the product of any two distinct elements is one less than a square. Notes and bibliography by Andrej Dujella. Diophantus Quadraticus On-line Pell Equation solver by Michael Zuker.

62. Solution Of A Diophantine Equation Solution of a diophantine equation. % dioph(+A, +B, +C, ?X0, ?Y0)is true if x = X0 + B * n and % y = Y0 A * n (for any integer http://perso.wanadoo.fr/colin.barker/lpa/dioph.htm

Solution of a Diophantine Equation LPA Index Home Page

63. Maths Glossary diophantine equation An equation which is required to be solved by integers.Thusthe diophantine equation 2x 2 3y 2 = 5 has the integer solution x=2,y=1 http://www.fortunecity.com/emachines/e11/86/mathglos.html

web hosting domain names email addresses Maths Glossary Algorithm : A fixed process which if caried out systematically produces a desired result.Thus the "Euclidean algorithm" is a set of rules which when applied to two integers produces their common divisor. Complex Number : A 2 dimensional number comprising a real and imaginary component of the form A+Bi,where i is the square root of -1.Such numbers are mapped on the Argand plane and form a matrix of numbers,the imaginary numbers being at right angles to the real ones.The conjugate takes the form a-bi. Continuum Hypothesis : In Cantorian set theory,the cardinal number of a set designates its "manyness". The cardinality of the set of integers 1,2,3,... is designated by .The cardinality of the set of real numbers is 2 .The continuum hyopothesis asserts that there is no set whose cardinal falls between and 2 Cube : 1. A number raised to the power 3,ie 2 x 2 x 2 = 2 2. A 3 dimensional figure with the height,width and depth having the same lengths,and all at right-angles to each other.

64. Generation5 - Genetic Algorithm Example: Diophantine Equation Home Articles Genetic Algorithms Beginner Genetic Algorithm Example DiophantineEquation By Samuel Hsiung and James Matthews, Printable Version. http://www.gamedev.net/reference/articles/article560.asp

Home Articles Reviews Interviews ... Contribute Login Login: Password: Keep me logged in. ( help Register Why register? Lost your password? ... Binary Decision Tree implementation in C++ Friends and Affiliates Home Articles Genetic Algorithms > Beginner Genetic Algorithm Example: Diophantine Equation By Samuel Hsiung and James Matthews Printable Version Make sure that you have read the genetic algorithms essay before reading this example. You also must have a working knowledge of C++ and object-oriented programming to utilize the classes and code examples provided. Genetic Algorithm Example Let us consider a diophantine (only integer solutions) equation: a+2b+3c+4d=30 , where a,b,c,d are positive integers. Using a genetic algorithm, all that is needed is a little time to reach a solution (a,b,c,d) . Of course you could ask, why not just use a brute force method (plug in every possible value for a,b,c,d given the constraints < a,b,c,d = )? The architecture of GA systems allow for a solution to be reached quicker since "better" solutions have a better chance of surviving and procreating, as opposed to randomly throwing out solutions and seeing which ones work. Let's start from the beginning. First we will choose 5 random initial solution sets, with constraints

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Guide : Diophantine Equations Global Metasearch Any Language English Afrikaans Arabic Bahasa Melayu Belarusian Bulgarian Catala Chinese Simplified Chinese Traditional Cymraeg Czech Dansk Deutsch Eesti Espanol Euskara Faroese Francais Frysk Galego Greek Hebrew Hrvatski Indonesia Islenska Italiano Japanese Korean Latvian Lietuviu Lingua Latina Magyar Netherlands Norsk Polska Portugues Romana Russian Shqip Slovensko Slovensky Srpski Suomi Svenska Thai Turkce Ukrainian Vietnamese Mode All Words Any Word Phrase Results Timeout Depth Adult Filter Add to Favorites Other Search Web News Newsgroups Images Guides Diophantine Equations ez2Find Home Directory Science Math ... Number Theory : Diophantine Equations Equal Sums of Like Powers Fermat's Last Theorem Web Sites [Site Info] [Translate] [Open New Window] Sets of numbers such that the product of any two is one less than a square. Diophantus found the rational set 1/16, 33/16, 17/4, 105/16; Fermat the integer set 1, 3, 8, 120. URL: http://www.weburbia.demon.co.uk/pg/diophant.htm Bibliography on Hilbert's Tenth Problem [Site Info] [Translate] [Open New Window] Searchable, ~400 items. URL: http://liinwww.ira.uka.de/bibliography/Math/Hilbert10.html

66. Applicatons - Solve Diophantine Equations Instructions This function will enable one to find all integer solutionsto the above equation, also known as a diophantine equation. http://archives.math.utk.edu/articles/atuyl/confrac/diaph.html

Solve Diophantine Equations A * X + B * Y = C where a,b, and c are given, non-zero integers Instructions: This function will enable one to find all integer solutions to the above equation, also known as a Diophantine equation In the space provided below enter the integer values of A,B, and C. When this is completed, press the bar below. The value of A: The value of B: The value of C: Main Introduction History Applications ... Credits

67. ThinkQuest : Library : Generation 5: The Artificial Intelligence Repository Sorry, JavaScript required for this. Genetic Algorithm Example DiophantineEquation. Genetic Algorithm Example diophantine equation. http://library.thinkquest.org/18242/gaexample.shtml

Index Artificial Intelligence Generation 5: The Artificial Intelligence Repository Will computers be able to function without humans in the future? This entry on Artificial Intelligence explores the history of AI and tells us what to look forward to in the future. Interviews with important people in the field are included. Various essays present topics such as Introduction to Natural Language Processing, Neural Networks, and Robotics. Visit Site 1998 ThinkQuest Internet Challenge Languages English Spanish German French Students Sam Lincoln Park Highschool, Chicago, IL, United States Edward Clear Lake High School, Houston, TX, United States Coaches Michael Clear Lake High School, Houston, TX, United States Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

68. Mathematical Programming Glossary Page 2 diophantine equations. A system of equations whose variables mustbe integervalued. A famous one is in Fermat s Last Theorem x http://carbon.cudenver.edu/~hgreenbe/glossary/second.php?page=D.html

69. Generation5 - Diophantine Equation Solver diophantine equation Solver By James Matthews, Printable Version. This is aC++ program that solves a diophantine equation using genetic algorithms. http://www.generation5.org/content/2000/diophantine_ga.asp

70. Diophantine Equations In Naturals -- References and Tomás, 1995 Miguel Filgueiras and Ana Paula Tomás, A fast method for findingthe basis of nonnegative solutions to a linear diophantine equation. http://www.ncc.up.pt/~apt/dioph/hdioph_1.html

References References Ana Paula, On Solving Linear Diophantine Constraints . Doctoral thesis, Universidade do Porto, 1997. and Filgueiras, 1997a] Proceedings of 8th Conference on Rewriting Techniques and Applications RTA'97 , Lecture Notes in Computer Science 1232, 269-283, Springer-Verlag,1997. Reviewed in Math Reviews and Filgueiras, 1997b] Progress in Artificial Intelligence EPIA'97 , Lecture Notes in Artificial Intelligence 1323, 73-84, Springer-Verlag, 1997. Reviewed in , 884.11020; (Reviewer J. Piehler) 11D04, 90C10. [Filgueiras Journal of Symbolic Computation , 19, 507-526, 1995. Reviewed in Math Reviews [Filgueiras Progress in Artificial Intelligence 6th Portuguese Conference on Artificial Intelligence , Lecture Notes in Artificial Intelligence 727, 297-306, Springer-Verlag, 1993. Reviewed in Math Reviews and Filgueiras, 1991a] Proceedings of the 5th Portuguese Conference on Artificial Intelligence , Lecture Notes in Artificial Intelligence 541, Springer-Verlag, 30-44, 1991. and Filgueiras, 1997c] COMPULOG NET Workshop on Constraint Programming and Filgueiras, 1993]

71. Lukol Directory - Science Math Number Theory Diophantine Equations Hilbert s Tenth Problem Given a diophantine equation with any number of unknownsand with rational integer coefficients devise a process, which could http://www.lukol.com/Top/Science/Math/Number_Theory/Diophantine_Equations/

Lukol Directory - Science Math Number Theory ... On the Psixyology of Diophantine Equations PhD thesis, Pieter Moree, Leiden, 1993. http://web.inter.NL.net/hcc/J.Moree/linkind2.ht... Diophantus Quadraticus On-line Pell Equation solver by Michael Zuker. http://www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.h... Fermat's Method of Infinite Descent Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4. http://sweb.uky.edu/~jrbail01/fermat.htm Diophantine Geometry in Characteristic p A survey by Jos?Felipe Voloch. http://www.ma.utexas.edu/users/voloch/surveylat... Pell's Equation Record solutions. http://www.ieeta.pt/~tos/pell.html Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n Methods to solve these equations. http://www.biochem.okstate.edu/OAS/OJAS/thiendo... Pythagorean Triples in JAVA A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2. http://home.foni.net/~heinzbecker/pythagoras.ht... Bibliography on Hilbert's Tenth Problem Searchable, ~400 items. http://liinwww.ira.uka.de/bibliography/Math/Hil...

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HOME WEBSEARCH SHOPPING ENTERTAINMENT ... Australian TV Guide NEW! Australian Movie Guide eCars.com.au Car Buyer/Seller AAMI Insurance Quotes Web categories Entertainment Lifestyle Reference Regional ... Number Theory : Diophantine Equations the entire directory only in Diophantine Equations Categories Equal Sums of Like Powers Fermat's Last Theorem Recommended websites Sets of numbers such that the product of any two is one less than a square. Diophantus found the rational set 1/16, 33/16, 17/4, 105/16; Fermat the integer set 1, 3, 8, 120. url: www.weburbia.demon.co.uk/pg/diophant.htm Bibliography on Hilbert's Tenth Problem Searchable, ~400 items. url: liinwww.ira.uka.de/bibliography/Math/Hilbert10.htm... Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n Methods to solve these equations. url: www.biochem.okstate.edu/OAS/OJAS/thiendo.htm Diagonal Quartic Surfaces Articles, computations and software in Magma and GP by Martin Bright. url: www.boojum.org.uk/maths/quartic-surfaces/ Diophantine Equations Dave Rusin's guide to Diophantine equations. url: www.math.niu.edu/~rusin/papers/known-math/index/11...

73. Diophantine Equations factorization diophantine equations. One important use of algebraicnumbers is to answer questions about diophantine equations. We http://mathcircle.berkeley.edu/BMC3/bamc/node3.html

Next: Read all about it! Up: bamc Previous: Unique and nonunique factorization Diophantine equations One important use of algebraic numbers is to answer questions about Diophantine equations. We have already seen one example of this (representing an integer as the sum of two squares); let's consider a few more examples. The equation is (mis)named ``Pell's equation''. Over , we can factor the left side and rewrite the equation as This makes clear the multiplicative structure of the set of solutions: if and are solutions, then Moreover, we can sort all solutions into increasing order by (which is an increasing function of for , given that ). Now it's easy to see that all solutions in positive integers are ``powers'' of the smallest solution, assuming that any solutions exist. There are several ways to show that solutions exist. One method uses continued fractions and has been known at least for 1000 years (it occurs in an old Indian text); it is probably the best method for explicitly computing solutions. ASIDE: What does this have to do with algebraic numbers? What we've done is to classify the algebraic integers in the field whose products with their conjugates equal 1. An analogous classification can be made for an arbitrary number field, which solves the Pell equation along the way. What about the equation

74. Section 1.1 From "Hilbert's Tenth Problem" By Yuri MATIYASEVICH 1.1 diophantine equations as a decision problem. Let us recall that a Diophantineequation is an equation of the form. D(x 1 , ,x m )=0,, (1.1.1). http://logic.pdmi.ras.ru/~yumat/H10Pbook/par_1_1.htm

Section 1.1 from the book "HILBERT's TENTH PROBLEM" written by Yuri MATIYASEVICH 1.1 Diophantine equations as a decision problem Let us recall that a Diophantine equation is an equation of the form D x x m where D is a polynomial with integer coefficients. In addition to (1.1.1), Diophantine equations can be written in the more general form D L x x m D R x x m where D L and D R are again polynomials with integer coefficients. When we speak of ''an arbitrary Diophantine equation,'' we shall have in mind an equation of the form (1.1.1) since an equation of the form (1.1.2) can easily be transformed into an equation of the form (1.1.1) by transposing all the terms to the left-hand side. However, we will often use the notation (1.1.2) for particular equations if this form turns out to be easier to grasp. We shall also take another advantage of the more general form (1.1.2); namely, in this case we can demand that D L and D R are polynomials with non-negative coefficients. Diophantine equations typically have several unknowns, and we must distinguish the degree of with respect to a given unknown x i and the ( total degree of (1.1.1), i.e., the maximum, over all the monomials constituting the polynomial

75. Omniseek: Family: Search Results For 'diophantine Equations' (http//math.la.asu.edu/~jj/445/chapters/euclid/euclid.html) Hilbert s Tenth ProblemRate This Site Given a diophantine equation with any number of unknowns http://family.omniseek.com/search/search.html?t=diophantine equations&mode=defau

76. SLCentral Directory - Science - Math - Number Theory - Diophantine Equations Developing A General 2nd Degree diophantine equation x^2 + p = 2^n Methods to solve these equations. » diophantine equations http://www.slcentral.com/directory/index.php/Science/Math/Number_Theory/Diophant

Site of the Week: Nokia 3560 Polyphonic Ringtones For ring tones motorola v60i phone Sunday 06 th June 2004 01:51 AM Advanced Search Recieve bi-weekly updates on news, new articles, and more Most Popular Links sony ericsson ringtones Polyphonic Ringtones For Sanyo free pat benatar ring tones Polyphonic Ringtones For Nokia Gift Ideas motorola i730 cell phone accessories free top up card numbers for virgin mobile phones Car Grills And Flaps MD Players ... Vaporizer Bong Other Stuff mini disc changers How To Make Braided Horse Tack motion alloy wheels Womens Fragrance Moschino ... Submit a Site SLCentral Directory - Science - Math - Number Theory - Diophantine Equations Equal Sums of Like Powers Fermat's Last Theorem This category in other languages: Spanish - Sets of numbers such that the product of any two is one less than a square. Diophantus found the rational set 1/16, 33/16, 17/4, 105/16; Fermat the integer set 1, 3, 8, 120. Bibliography on Hilbert's Tenth Problem - Searchable, ~400 items. Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n - Methods to solve these equations. Diophantine Equations - Dave Rusin's guide to Diophantine equations.

77. BOUNDS FOR SMALL PRIME SOLUTIONS OF SOME DIOPHANTINE EQUATIONS BOUNDS FOR SMALL PRIME SOLUTIONS OF SOME diophantine equationS. Prof. MC Liu. Departmentof Mathematics HKU518/96P. 1. STORY OF THE PROBLEM AND OUR MAIN RESULTS. http://www.hku.hk/rss/res_proj/54/54.htm

BOUNDS FOR SMALL PRIME SOLUTIONS OF SOME DIOPHANTINE EQUATIONS Prof. M.C. Liu Department of Mathematics HKU518/96P 1. STORY OF THE PROBLEM AND OUR MAIN RESULTS In 1967 A. Baker considered the Goldbach-Vinogradov type equation (1), where m and a j are certain integers and all p j are primes (i.e., prime numbers). When not all a a a are of the same sign (e.g., a 1 and a -1) he pioneered a series of deep problems. One of these is to obtain the best possible bound in terms of a a a and m for small prime solutions P P and P of the above equation (1). We call this problem the Baker Problem In fact, we obtained the best possible form for the bound of small prime solutions P P P of the above equation (1) with the numerical values of the constants in the bound unspecified. The essential part of the bound we obtained in 1989 is where B After our work of 1989, attention is focused on the value of the constant B since it is the last unknown as well as an essential part in the Baker Problem.

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Diophantine Equations JasperGifts.com Shopping? It's all here! Shopping Contact Top Trade ... Webmasters Search Aromatherapy Baby Bath and Body Bed and Bath ... diophantine equation linear Links: Science: Math: Number Theory: Diophantine Equations Home Science Math Number Theory : Diophantine Equations Subcategories: Equal Sums of Like Powers Fermat's Last Theorem Diophantine Equations- More Web Results Below Add Your Site or modify Bibliography on Hilbert's Tenth Problem Searchable, ~400 items. Diophantine Equations Dave Rusin's guide to Diophantine equations. Egyptian Fractions Lots of information about Egyptian fractions collected by David Eppstein. Linear Diophantine Equations A web tool for solving Diophantine equations of the form ax + by = c. The Erdos-Strauss Conjecture Featured Gift Idea: SoulPaks™ Gifts? Send SoulPaks! FREE SHIPPING! SoulPaks feature items for the 5 senses. Custom-build and send for corporate and personal gift occasions. Search Engine Tickets Collectibles Search ... Web Directory ThisIsOurYear JasperGifts.com ©JasperGifts.com 2004

79. Section 2.3: Linear Diophantine Equations 1 one goal of this chapter is to develop a systematic method for finding all integersolutions x and y (when there are any) to the linear diophantine equation. http://www.mathlab.mtu.edu/COURSES/holt/dnt/euclid3.html

2.3 Linear Diophantine Equations 1 As stated in the Prelab section, one goal of this chapter is to develop a systematic method for finding all integer solutions x and y (when there are any) to the linear diophantine equation a x b y c where a b , and c are integer constants. As you discovered when working on the Prelab exercises, for a given choice of a and b , equation (1) may have several solutions or possibly no solutions; it depends on the value of c . If we have specific values for a and b , how can we figure out the values of c for which equation (1) will have a solution? As a first step, let's look at the situation for a specific choice of a and b , say a = 6 and b = 4. In this case, the above equation becomes x y = c and our question is: For what values of c is there a solution to this equation? One way to approach this is to try plugging a bunch of different values for x and y into the left-hand side of (2), and see what we get out. After all, any value that comes out must be a suitable value for

80. Solving A System Of Linear Diophantine Equations With Lower And And .. Aardal, Hurkens, Lenstra (1998) (Correct) 14.8% An Algorithmfor Solving a diophantine equation With.. - Aardal, Lenstra http://citeseer.ist.psu.edu/329160.html

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